Results 11 to 20 of about 65 (58)
The elliptic sieve and Brauer groups
Proceedings of the London Mathematical Society, Volume 126, Issue 6, Page 1884-1922, June 2023., 2023 Abstract A theorem of Serre states that almost all plane conics over Q${{\mathbb {Q}}}$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve for elliptic curves.
Subham Bhakta +3 more
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On the Brauer group of a generic Godeaux surface
Journal of the London Mathematical Society, Volume 107, Issue 5, Page 1881-1899, May 2023., 2023 Abstract Let X$X$ be a Godeaux surface and qX:Y→X$q_{X}\colon Y\rightarrow X$ be its universal cover. We show that the pullback map qX∗:Br(X)→Br(Y)$q_{X}^{*}\colon \operatorname{Br}(X)\rightarrow \operatorname{Br}(Y)$ is injective if ρ(Y)=9$\rho (Y)=9$. Our arguments rely on a degeneration technique that also applies to other examples.
Theodosis Alexandrou
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Some torsion classes in the Chow ring and cohomology of BPGLn
Journal of the London Mathematical Society, Volume 103, Issue 1, Page 127-160, January 2021., 2021 Abstract In the integral cohomology ring of the classifying space of the projective linear group PGLn (over C), we find a collection of p‐torsion classes yp,k of degree 2(pk+1+1) for any odd prime divisor p of n, and k⩾0. If, in addition, p2∤n, there are p‐torsion classes ρp,k of degree pk+1+1 in the Chow ring of the classifying stack of PGLn, such ...
Xing Gu
wiley +1 more source
More on the Schur group of a commutative ring
International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 2, Page 275-282, 1985., 1985 The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group of R which contain a homomorphic image of a group ring RG for some finite group G. It is the purpose of this article to continue an investigation of this group which was introduced in earlier work as a natural generalization of the Schur group of a field.
R. A. Mollin
wiley +1 more source
Glider Brauer-Severi varieties of central simple algebras
Journal of Algebra, 2020 24 pages, submitted for ...
Frederik Caenepeel, Fred Van Oystaeyen
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Witt groups of hermitian forms over a Brauer–Severi variety [PDF]
Pacific Journal of Mathematics, 2010 Let \(k\) be a field with \(\text{char}\,k \neq 2\), let \(X\) be a scheme such that \(2 \in H^0(X, {\mathcal O}_X^*)\), and let \({\mathcal A}\) be an algebra over the scheme \(X\) with a \({\mathcal O}_X\)-linear involution \(\sigma\) (here an \({\mathcal O}_X\)-algebra is always assumed to be an associative \({\mathcal O}_X\)-algebra that is unital ...
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Galois invariants of finite abelian descent and Brauer sets
Bulletin of the London Mathematical Society, Volume 56, Issue 10, Page 3240-3256, October 2024.Abstract For a variety over a global field, one can consider subsets of the set of adelic points of the variety cut out by finite abelian descent or Brauer–Manin obstructions. Given a Galois extension of the ground field, one can consider similar sets over the extension and take Galois invariants.
Brendan Creutz +2 more
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Arithmetics of homogeneous spaces over p$p$‐adic function fields
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract Let K$K$ be the function field of a smooth projective geometrically integral curve over a finite extension of Qp$\mathbb {Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local–global and weak approximation problems for homogeneous spaces of SLn,K$\textrm {SL}_{n,K}$ with geometric stabilizers ...
Nguyen Manh Linh
wiley +1 more source
Constructions of Brauer-Severi Varieties and Norm Hypersurfaces
Canadian Journal of Mathematics, 1990 Let k be any field, A a central simple k-algebra of degree m (i.e., dimk A = m2). Several methods of constructing the generic splitting fields for A are proposed and Saltman proves that these methods result in almost the same generic splitting field [8, Theorems 4.2 and 4.4].
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Universal Brauer-Severi varieties
33 pages, some typos corrected, reference to work of Uriya First ...
Gounelas, Frank, Huybrechts, Daniel
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